Forecasting a future value typically involves deriving a mathematical model from a set of measurements taken over a period of time and using the model to forecast future values. Such forecasts are particularly useful in business, for example, to ensure that the demand for goods can be met by the existing inventory of goods or the likely volume of produced goods. A sales organization of a business may use inventory forecasts to ensure that sufficient inventory exists to meet future orders. As a further example, a delivery organization of a business may use inventory and/or other forecasts to schedule delivery of existing orders.
Over the years, techniques have been proposed to generate forecasting models based on a fixed polynomial or Fourier series variation of values over time. In most cases, model parameters are generated by minimizing the residual sum of squares based on the assumed fixed polynomial or Fourier series variation. Such models, however, fail to provide accurate forecasts of future values when the underlying measurements either have seasonal variations or when the data set containing the measurements includes extreme outliers, non stationary noise, or discontinuities.
In view of the above drawbacks, there is a need for improved systems and methods for forecasting future values, including systems and methods for generating forecasting models that can account for both seasonal variations and extreme outliers. There is also a need for improved systems and methods for generating such forecasting models by simultaneously including the most recent actual measurements or data and minimizing the computation cost of generating model parameters. In addition, there is a need for improved techniques for identifying and removing outliers from the measurements to generate a more accurate forecasting model.